Study of BlackJack

Rules

In Blackjack, there is a dealer and one or more players which their objective is to get more points than the dealer without going over 21 which is called ‘busting’.

The player wins if they do not bust and their total value is greater than that of the dealer.

First a bet is placed by the player which whoever wins gets to get both bets. Both player and the dealer are dealt two cards each but one of the dealer’s cards is placed face down so that the player does not know if their total value is greater or lower than the dealer. When the player ‘stands’, meaning they stop hitting, the dealers card will be shown.

Now, if the player’s value is greater than that of the dealer, the dealer will draw one more card. If the player’s value is still greater or the dealer busts, the player wins.

If both values are the same, it is called a ‘push’ and everyone gets his bet back. If the dealers value is greater than that of the player, the player losses.

A soft hand is when the player has an Ace. The Ace can be played as a value of 1 or 11. Therefore in many cases the player can still hit without busting, because if they exceed 21 the value of the ace will now become 1.

Doubling is when after you are dealt your cards you decide to double the bet and you are dealt another card face down. You are no longer entitled to hit after doubling.

Split is when the player has two identical cards at the beginning of the round they are offered to if they want to play them a separate hand. If the player accepts an additional card is dealt on each hand.

(Cornell, 2016)

Insurance is “when the dealer draws a face-up ace; at this point, the dealer will go around the table and ask everybody if they want to take insurance. The insurance is in case the dealer receives a blackjack, and you put out half of your original bet as the insurance. Assuming the dealer does have a blackjack, you win 2-1 on your insurance wager” (Blackjack Life, 2016).

Different Player Strategies

Wizards Simple Strategy (Shacklefrod, 2016):

• 8 or less points just hit

• If you have 9:

• If the dealer has a small card (2 - 6) double your bet.

• If the dealer has a big card (7 - Ace) hit.

• If you have 10 or 11

• Double if you have more points than the dealer

• If you have 12 to 16

• Stand if the dealer has a small card

• Hit if the dealer has a big card

• Soft Hands (Having an Ace in your hand)

• 15 or less always hit

• 16 - 18:

• Double if the dealer has a small card

• Hit if the dealer has a big card

• Splits:

• 2's, 3's, 6's and 7's should be split if the dealer has a small card

• Always split 8's and Aces.

• Never split 4's, 5's and 10's

• Surrender 16 vs dealers 10.

Basic Strategy and Martingale Betting System (americancasinoguide, 2011):

Basic Strategy

Any good blackjack player should memorize the basic strategy chart. You can cut the house advantage to 0.25% by using this strategy

He also mentions that basic strategy is a very good way of playing blackjack but will never overcome the house edge by itself.

Never take insurance since it is always a risky bet, unless you are counting cards which you have a higher possibility to know if the card dealt might have a high number.

There are several charts for the different numbers of deck which you can find listed here: http://wizardofodds.com/games/blackjack/basics/#toc-BasicStrategy

The images below show a 1 deck basic strategy chart.

Martingale Progressive Betting System

Every time you lose a bet, you double it the next time. So, once you win, you will always win back what you lost and a one dollar extra

Disadvantages are that no matter how much money you have, eventually if you keep on losing, you will not be able to double the bet.

Most of the players believe that the martingale is a good strategy because most of the time it works, but if at any time, you hit that point where you can no longer double, you would have lost everything you won.

Computer simulations have proven that betting system cannot survive a long term winning and can never overcome the housing advantage. Shacklefrod adds that all betting systems are scams and you should never pay for a book promoting one.

Long Term winning:

Shacklefrod suggest card counting as the most effective.

He also mentions that basic strategy is a very good way of playing blackjack but will never overcome the house edge.

Card Counting: High/Low Card Count (Blackjack Apprenticeship, 2016):

Card counting is when you keep track of how much good cards (10 to ace) are remaining in the deck over bad cards (2 - 6). This is done by assigning a value to each card and keep track of the total number.

Counting Value:

• Cards from 2 to 6 = +1

• Cards from 7 to 9 = 0

• Cards from 10 to King including Ace = -1

Every time a card is dealt you count. If the count is positive meaning that the next card dealt have a greater chance of being a high card, you bet higher while if the counter is negative you bet less.

Keeping a running count:

• On all cards on the table including the dealers and other players.

• Count until the dealer shuffles the cards again

• If the running count is towards positive, your chance of winning is higher

• If the running count is negative, then you are more likely to lose.

True Count

Since today casinos are using multiple decks to decrease card counting you should divide the score by the number of decks to get the true count.

Example if the count is +10 and there are two decks, then the true count is +5

Maths Behind it (Mathsisfun, 2016):

The game does not reset completely after each round instead you know if the remaining are good cards (10, J, Q, K. A) or bad cards (2 ,3 ,4 ,5 ,6) from those discarded.

The method used is called conditional probability

For every negative count the house edge goes up by approximately 0.5% and vice versa

Conditional Probability:

• Independent events:

• The event is not affected by any other events – toss of a coin

• Perfectly isolated thing

• What happened before will not affect what is going to happen in the next event

• The chance is 50%

• Dependent Events:

• Events that are affected by previous events – Bag with marbles

• Chance changes every time you draw out a marble

• This can be either negative or positive depending on what you draw first

Notation of Probability:

Formula:

P(A and B) = P(A) x P(B|A)

Where:

P(A) is the probability of event A

P(B|A) is the event B given event A

Example in Blackjack what is the probability of drawing an Ace, using only one deck, on the first two card draws?

There are 52 cards in a deck and 4 of them are aces.

Therefore, the probability of getting an ace on the first draw is 4/52 or

P(A) = 4/52

If you manage to draw an ace on the first draw the chance of drawing an ace on the second round is less 3/51 or

P(B|A) = 3/51

By using the formula:

P(A and B) = P(A) x P(B|A) = (4/52) x (3/51) = 12/2652 = 1/221

The chance of getting 2 aces is 1 in 221, or 0.5%

Analysis

As a gambling game Blackjack is a rather simple game to understand. The rules and objectives are strait forward; do not go over 21 and get a higher value then the dealer. But in reality, as the research shows, the mechanics behind the game are rather complex and the game can be turned from luck to prediction.

To master counting one has to be fast in calculations and in assigning the value to the card. On top of that if you are not the only player playing against the dealer, you have to keep into consideration other players cards as well. The counting method is rather simple, you should add plus one for every card from rank two to rank six, ignore cards from rank seven to rank nine, and subtract one from rank ten to the king’s rank.

Keeping count is done to know how much good cards are available in the deck and therefore you can increase or decrease your betting accordingly. So, if a card from two to six is drawn you have removed a bad card from the deck and increasing the chance of getting a card with a higher level. Said that, it is very hard to keep track of the count and today casinos are also increasing decks to make it even harder.

This gave me an inspiration in designing a gambling game based on the counting of Blackjack. Every time you draw a low value card you will be rewarded while if you get a high value card you will be punished. But first I need to explore more the player experience and what do they seek.

Player Experiences and Different types:

Explorer and Achiever

I found this player who is documenting the journey while playing black jack and from time to time other players also share their experiences.

The player nicknamed Windar (WINDAR, 2008) explains how it all started from a purchase of a cheap DVD talking about how to play Blackjack. Windar took it very seriously and studded hard until he felt ready to hit the casino.

From his first experience, he learned that he should stop playing when he gets board. He was making profit when he got bored and still continued playing. Not interested in the game anymore he made a lot of mistakes which led him to lose all of his money. His first remark is to not to play if you are board.

The second time he visited the casino, he showed off to his friends how good he was but by the time they went to the casino he was dead tired and did not manage to concentrate enough and ended up almost losing everything as well. He made a rebound at the last few minutes when he says he woke up and turned a $50 to $240.

I can relate to him playing other games bored and tired. If I get bored while playing a game, and I still continue playing, it’s just a waste of time. You are just playing to pass the time instead of doing something else, and usually your gameplay is as if you do not care anymore of dying and losing. This could be as a goal to game designers of keeping the game interested, since board players will leave the game. Obviously, everyone can have a bad day and not in the mood to play or after a long time of playing they get tired, but the more engaging the game the better chance of keeping the player playing.

I do not play gambling games, but competitive games I like, require full concentration to have sharp reflexes and accuracy. If I am tired, no matter how much focused I think I am, I still get to react slower than my opponent or do not think of the right strategy as our character Windar. This is an advantage for the casino in gambling games. If the players are not concentrated they tend to lose more and maybe that is the reason why they serve alcoholic drinks. What I am going to say now might sound in human but I am trying to evaluate both sides and a strategy the casino can use is to give free drinks once in a while to winning players to make them lose concentration. It would be another game while playing games, but it is still up to the player if he decides to drink it or not.

Windar takes it much more seriously and studies and buys several other books along his journey. He says that he is not a card counter and that he will never be. In our research, we found out that the house edge of the casino is of 2% and Windar also mansions this, he says that a card counter reaches up to 48% against the other 52% of the casino which for him is still low. He claims that with his two-system strategy he beats the casino more than 50% and sometimes even more than 60% which for him is a good enough reason on not becoming a card counter.

We can clearly see that Windar is a strategic player and plays to win not to pass time or for the trill of gambling. Thus, Windar is an achiever player type (Extra Credits, 2015). But we can also identify that he is an explorer as well where he continuously takes interest in game mechanics and studies on strategies of the game. To be fair this theory was first studded on multiplayer games but today it is used to define all types of players, weather it is good or not I do not know, but in this case, it does make sense. Windar is exploring and studying a lot about the game to try and get the highest score possible which also makes him the achiever.

Achievers (Card counters):

This is about a team of card counters who teamed up to earn money. An interview to Colin Jones was made in order to sum up their overall experience (americancasinoguide, 2012).

We can see a total different game play from Windar. They got inspired from reading a book about gambling which mentioned card counting. Initially, there was no team but they used to play for themselves. They soon found themselves lonely so they started to talk on the phone constantly about the game and eventually they ended teaming up. Here, we already see a different approach, socializing, where in Winders case was not present. Therefore, gambling games can also be socializing. They ended up putting a larger team together where they would share their resources and knowledge.

In this case, we do not see exploration of the game but instead they stick to card counting as their only one strategy. In their documentary, they talk about winning Millions but in some years, they also lost a lot of money.

Casual Players

Unlike other player, this type of player uses blackjack as a trill. They do not have any strategy at all or basic ones but are not willing to explore any further.

I started observing a player called Croupier (Croupier, 2016) playing balck jack. He has several videos and by observing him it was hard to tell if he had any strategy at all; Its not that clear to me how he actually plays, seems pretty much based on instincts. He plays differently all the time and stands where I would have hit one more. He also seems to be there for socializing, he is continuously chatting with dealers and other players.

Playing just by instinct it is surprising to see how lucky the dealer gets. Sometimes I would have bet that Croupier had won with a value of twenty and then, out of surprise, the dealer hits 21!

Gambling games can be approached in different ways, achievers, explorers and or socializers. There is no room for killers since you are just playing against the dealer. Just for the information, a killer type player is one who impacts on other players and enjoy themselves seeing other players frustrated and down on their knees to the killer’s mercy.

Referencing

americancasinoguide, 2011. How to win at blackjack (21) with gambling expert Michael "Wizard of Odds" Shackleford. [Online] Available at: https://www.youtube.com/watch?v=YkUsN-GNCSY [Accessed 30 November 2016].

americancasinoguide, 2012. Christian Blackjack Card Counting Team Co-Founder, Colin Jones, Interview. [Online] Available at: https://www.youtube.com/watch?v=vg1U8ib4Zs4 [Accessed 30 November 2016].

Beating Casino, 2015. How to Count Cards in Blackjack - High Low Card Counting. [Online] Available at: https://www.youtube.com/watch?v=9UE0FMidxw4 [Accessed 30 Novmber 2016].

Blackjack Apprenticeship, 2016. How To Count Cards in Blackjack and Bring Down the House. [Online] Available at: https://www.blackjackapprenticeship.com/resources/how-to-count-cards/ [Accessed 30 November 2016].

Blackjack Life, 2016. Blackjack Insurance – A Bad Bet. [Online] Available at: http://blackjacklife.com/blackjack-insurance-a-bad-bet/ [Accessed 30 November 2016].

Cornell, M., 2016. Blackjack. [Online] Available at: http://www.math.cornell.edu/~mec/2006-2007/Probability/Blackjack.htm [Accessed 30 November 2016].

Croupier, 2016. croupiercasino. [Online] Available at: https://www.youtube.com/channel/UC-HlSAHcXOQPOVoXOciGYDg [Accessed 30 November 216].

Extra Credits, 2015. Bartle's Taxonomy - What Type of Player are You?. [Online] Available at: https://www.youtube.com/watch?v=yxpW2ltDNow [Accessed 30 November 2016].

Mathsisfun, 2016. Conditional Probability. [Online] Available at: http://www.mathsisfun.com/data/probability-events-conditional.html [Accessed 28 November 2016].

Shacklefrod, M., 2016. Blackjack - Wizard of Odds. [Online] Available at: http://wizardofodds.com/games/blackjack/basics/#toc-Wizard27sSimpleStrategy [Accessed 30 November 2016].

Shi, D., 2014. What is the mathematics behind card counting in Blackjack?. [Online] Available at: https://www.quora.com/What-is-the-mathematics-behind-card-counting-in-Blackjack [Accessed 30 November 2016].

Vosko, S., 2010. Mathematics and Card Counting in Blackjack. [Online] Available at: https://prezi.com/zjqtcdbrumd-/mathematics-and-card-counting-in-blackjack/ [Accessed 30 November 2016].

WINDAR, 2008. Your Experiences - HitorStand Blackjack Message Board. [Online] Available at: http://hitorstand.net/forum/discussion/5182/your-experiences/p1 [Accessed 30 November 2016].